If
there's one thing for sure about gamers, they love their polyhedron dice. Every
gamer I know has purchased more than one set of Poly's. Even people like me, who
play mostly GURPS, have more than one set of dice. I even bought a weird
set of dice which included a d3, d5, d7, d16, d24, and d30 (pictured to the
right). There's just something
about those little platonic
solids, and even the non-platonic ones, and once you have those dice you want to use them, which I don't really get a a chance to do with GURPS.
Here I give some advice on using Polyhedral dice with GURPS.

The most important roll in GURPS, and the one you will do the most, is
rolling 3d6. This is used for all skill checks, attribute checks, disadvantage
Self-Control rolls, rolling on the Freight Check table and on the Reaction
Table. Thus it is the most obvious place to do a little switcheroo. The easiest
switch is to roll 1d4+1d6+1d8 instead of rolling 3d6. Or, if you have the weird
set of die you can use 1d5+1d6+1d7. This will change the shape
of the bell curve slightly, and increases the chances of rolling the extremes
(3-6, 15-18) slightly while decreasing the chances of rolling the central values
(8-13) slightly. However, these changes are all small, less than 1% difference,
making it a great place to do a simple change which gives the game a vastly different
feel.

Die

Avg.

d3

2

d4

2.5

d5

3

d6

3.5

d7

4

d8

4.5

d10

5.5

d12

6.5

d16

8.5

d20

10.5

d24

12.5

d30

15.5

For damage rolls there's a few ways you can convert them. Each +1 to damage
moves a die up one step from 1d4 to 1d6 to 1d8 to 1d10 to 1d12. So 2d6+1 yields
the same average as 1d6+1d8. Similarly, each -1 moves the dice down one step.
These can even be combined, turning 2d6 into 1d4+1d8. And like the skill roll,
you can always convert 3d6 into 1d4+1d6+1d8. You could then use +1's to convert
the dice into something higher, for example 3d6+3 could be 3d8, or even
1d6+1d8+1d10.

A second option is to find the average damage for a specific roll by
multiplying the number of dice by 3.5, then adding or subtracting any bonuses or
penalties to the roll. For example, 3d6+3 averages to (3×3.5)+3=10.5+3=13.5.
From there you just need to figure out the best dice to use for the conversion
and can subtract, in this case it's a little over a d24, so you could use 1d24+1
since the average of 1d24 is 12.5, adding +1 to that results in the same 13.5
average. It also happens to be 3×4.5=13.5, which is the average result of
a 3d8. 2×6.5=13 is the average of 2d12, which is just below the target
number we're looking for. Generally, when converting dice I recommend using at
least two dice, so I would would recommend using 2d12 or 3d8 over 1d24+1.

Another option is that you can use or create a standardized conversion table like the one I provide
below to help you convert damage dice rolls
into a polyhedron roll. I purposely didn't use the weird dice on the table
because most gamers are unlikely to have them, but on your own table you could
use them.

In general I would also suggest that you do all the
conversions away from the gaming table, and if a new damage needs to be figured out
in-game just use the standard GURPS rules using d6's until you have a chance to convert it away from the game.
It'll make things less confusing.